National Chengchi University
Test Bank
Chapter 2
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Chapter 3
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Chapter 4
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Chapter 5
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Chapter 6
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Answer:
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Chapter 8
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Chapter 9
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Chapter 10
1. The National Collegiate Athletic Association (NCAA) restricts the amount that colleges and universities may pay their student athletes. Suppose that there are just two colleges in the NCAA -- Ivy and State. Each must choose between paying athletes according to NCAA rules or paying more.
a. Construct a game in strategic form to analyze the choices of Ivy and State.
b. Identify the equilibrium/equilibria.
c. The NCAA rules have government backing. How will this affect the equilibrium or equilibria?
Answer:
a) The key to this question is constructing the game in strategic form. The NCAA functions as a buyer cartel in the market for college athletes. If both Ivy and State pay according to NCAA rules, then they succeed as a cartel – they receive 3 each. If Ivy breaks the cartel and pays more, while State keeps to the cartel, then Ivy will benefit and State will lose – Ivy gets 4, and State gets 1. Similarly, if Ivy keeps to the cartel and State breaks it, Ivy gets 1 and State gets 4. Finally, if they both pay more, then both will be worse off – each receives 2.
| |State College |
| |Pay by NCAA rule |Pay more |
|Ivy College |Pay by NCAA |I: 3, |I: 1, |
| | | | |
| | |S: 3 |S: 4 |
| |Pay more |I: 4, |I: 2, |
| | | | |
| | |S: 1 |S: 2 |
b) The Nash equilibrium is both colleges will pay more than the NCAA allows.
c) If the NCAA has government backing, then both colleges will follow the NCAA recruiting rules, and achieve the highest combined profit.
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6. The demand for most new films peaks in the first few days after opening, then tapers off. Two key factors that affect potential demand are the season (Summer and Christmas are the best times) and the timing of other releases. Suppose that both Studio Luna and Moonlight Movies are producing major action movies. The two studios must choose between release on December 11 or 18. If both films open on December 11, each will sell 200,000 tickets. If one opens on December 11 and the other on December 18, then the early release will sell 350,000 tickets, while the later release will sell 150,000. If both open on December 18, each will sell 100,000 tickets.
a. Suppose that the studios choose their launch dates simultaneously. Construct a game in strategic form to illustrate the situation and identify the equilibrium or equilibria.
b. Is this a zero-sum game?
c. Is this a situation of first-mover advantage? Explain your answer with a suitable game in extensive form.
Answer:
a) There is one Nash equilibrium: both studios open on December 11.
| |MOONLIGHT |
| |Open Dec 11 |Open Dec 18 |
|LUNA |Open Dec 11 |L: 200,000 | L: 350,000 |
| | | | |
| | |M: 200,000 |M: 150,000 |
| |Open Dec 18 |L: 150,000 | L: 100,000 |
| | | | |
| | |M: 350,000 |M: 100,000 |
(b) This is not a zero sum gain, because one party’s gain is not equal to the other party’s loss.
(c) If Luna moves first, the extensive form of the game is:
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Regardless of the probabilities of Moonlight’s choice, Luna will prefer to open on Dec. 11. The game facing Moonlight is comparable: regardless of the probabilities of Luna’s choice, Moonlight should choose Dec. 11. Thus, there is no first mover advantage, the equilibrium involves both choosing Dec. 11, regardless of whether they choose simultaneously or sequentially.
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Luna
Dec. 18
Dec. 11
Moonlight Dec. 18 L: 100,000
Moonlight Dec. 11 L: 150,000
Moonlight Dec. 18 L: 350,000
Moonlight Dec. 11 L: 200,000
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